Problem: Find the zeros of the function. Enter the solutions from least to greatest. $f (x)=(-x -2)(-2x -3)$ $\text{lesser }x = $
Explanation: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(-x -2)(-2x -3)=0$. So either $(-x -2)=0$ or $(-2x -3)=0$ : $\begin{aligned} (1)&&-x -2&=0 \\\\ &&-x&=2 \\\\ &&x&=-2 \end{aligned}$ $\begin{aligned} (2)&&-2x -3&=0 \\\\ &&-2x &= 3 \\\\ &&x&=-\dfrac{3}{2} \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -2 \\\\ \text{greater } x &= -\dfrac{3}{2} \end{aligned}$